Since the scuba diver jumps into the water and decreases his altitude by 5.6 meters in one minute, the equation that can be used to represent the divers altitude is [tex]y = -5x + 1.3[/tex]
What is the eqquation?The standard equation is [tex]y = mx + b[/tex]
y,x = variables
m = rate of change
b = initial value of y.
y = the height of the scuba driver after x minutes.
Given that b = 1.3
m = -5.6(decrease in altitude)
Then the equation can be written as ; [tex]y = -5x + 1.3[/tex]
hence scuba driver height is given by the equation [tex]y = -5x + 1.3[/tex]
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missing options;
A.
1.3 + 5.6
= 6.9
B.
-1.3 + 5.6
= 4.3
>
O
C. 1.3+(-5.6) = – 4.3
>
O
D. -1.3+(-5.6) = -6.9
The equation that represents the scuba diver's altitude after jumping into the water is y = 1.3 - 5.6t, where y is in meters and t is in minutes.
Let y represent the diver's altitude in meters relative to sea level after t minutes. Initially, at sea level, we have y(0) = 1.3. Due to the descent in water, the altitude decreases by 5.6 meters per minute, which means the altitude change per minute can be represented by
-5.6t. Thus, the equation that can be used to represent the diver's altitude as a function of time is:
y = 1.3 - 5.6t
where y is in meters and t is in minutes.
Which lines in the graph have a slope greater than 1 but less than 2?
line 1
line 2
line 3
line 4
line 5
Answer:
line 1 line 3
Step-by-step explanation:
I took the test
Using full sentences, explain the solution for 0^-1
Answer:
There is no solution.
0^-1 = 1/0
You can't divide by 0; therefore, there is no solution because the solution is undefined.
Zero to the power of negative one can be rewritten as one over zero. This fraction is technically equal to infinity, though it is also undefined.
Plz help!!!!!!!!!!!!
Answer:
-8
Step-by-step explanation:
(-32)^(3/5) is equivalent to (-2^5)^(3/5) and applying exponent rules then simplifying you can get your answer.
Answer:
Step-by-step explanation:
Let's just see what happens if we do
(-32)^(1/5)
That means what number do you start with that when multiplied 5 times gives you - 32?
The answer is - 2
-2 * - 2 * -2 * -2 * -2 = -32
Now when you have a root sign that goes to the 1/5 power, you can take out 1 of the factors and throw the other 4 away.
[tex]\sqrt[5]{-2 * - 2 * - 2 * -2 * -2} = - 2[/tex] take one - 2 from under the root sign and throw the other 4 away
That's not the answer. We have one more step.
What is -2 to the 3rd power.
(-2)^3 = - 8
So the answer is -8
[tex]\sqrt[5]{- 32}^3 = -8[/tex]
A cheetah runs at a speed of 49 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?
To find the total distance, multiply the speed by the number of hours.
The equation would be d = 49t
The slope of the line passing through the points (-2,6) and (6,4) is
Answer:
[tex]-\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]rule of slope = \frac{y^2-y^1}{x^2-x^1}[/tex]
4 - 6 = -2
6 - -2 = 8
-2 ÷ 8 = -0.25 (-1/4)
Answer:
The slope is [tex]-\frac{1}{4}[/tex]
Step-by-step explanation:
Let [tex](x_1,y_1)=(-2,6)[/tex] and [tex](x_2,y_2)=(6,4)[/tex].
The slope of the line passing through these two points is given by;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute the values to obtain;
[tex]m=\frac{4-6}{6--2}[/tex]
[tex]m=\frac{-2}{8}[/tex]
[tex]m=-\frac{1}{4}[/tex]
Solve –3(2 – 5w) = 9w + 66 for w.
Let's solve your equation step-by-step.
−3(2−5w)=9w+66
Step 1: Simplify both sides of the equation.
−3(2−5w)=9w+66
(−3)(2)+(−3)(−5w)=9w+66(Distribute)
−6+15w=9w+66
15w−6=9w+66
Step 2: Subtract 9w from both sides.
15w−6−9w=9w+66−9w
6w−6=66
Step 3: Add 6 to both sides.
6w−6+6=66+6
6w=72
Step 4: Divide both sides by 6.
6w
6
= 72
6
w=12
Answer:
w=12
What is (f+g)(x)? f(x)=x^2-36 g(x)=x^3+2x^2-10
Answer:
x³ + 3x² - 46
Step-by-step explanation:
note that (f + g)(x) = f(x) + g(x)
f(x) + g(x)
= x² - 36 + x³ + 2x² - 10 ← collect like terms
= x³ + 3x² - 46
True or false: both functions and relations can be represented by mapping diagrams
Answer:
Step-by-step explanation: the answer is true
The given statement is true. Both functions and relations can be represented by mapping diagrams is true statement.
Mapping diagrams: A mapping diagram is a visual representation that shows the relationship between the elements of a domain and the corresponding elements in a co-domain or range.
Functions: A function is a specific type of relation where each element in the domain is mapped to exactly one element in the co-domain. In a mapping diagram for a function, each element in the domain is represented by an arrow pointing to its corresponding element in the co-domain.
Representing functions with mapping diagrams: To represent a function using a mapping diagram, follow these steps:
Identify the elements in the domain and co-domain of the function.
Draw a set of arrows from each element in the domain to its corresponding element in the co-domain.
Make sure that each element in the domain has only one arrow pointing to it from the co-domain, indicating the one-to-one mapping characteristic of functions.
Relations: A is a more general concept that describes any set of ordered pairs consisting of elements from a domain and co-domain. A relation can have multiple outputs for a single input, unlike a function.
Representing relations with mapping diagrams: To represent a relation using a mapping diagram, follow these steps:
Identify the elements in the domain and co-domain of the relation.
Draw arrows from each element in the domain to all the corresponding elements in the co-domain, representing the multiple outputs or mappings.
In summary, mapping diagrams can be used to represent both functions and relations. Functions have a one-to-one mapping, whereas relations can have multiple mappings for a single input. Mapping diagrams provide a visual way to understand and represent the relationships between the elements of a domain and co-domain.
Therefore, the given statement is true. Both functions and relations can be represented by mapping diagrams is true statement.
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The price of a movie ticket was $6.75 in 2010 and $8.00 in 2013.Find the approximate percent increase in the price of the ticket.
A) 18.5%
B) 20.2%
C) 21.5%
D) 19.4%
E) 22.8
The approximate percent increase in the price of the movie ticket is 18.52%.
Explanation:To find the approximate percent increase in the price of the movie ticket, we can use the formula:
Percent increase = ((New price - Old price) / Old price) * 100
Plugging in the given values:
Percent increase = ((8.00 - 6.75) / 6.75) * 100 = 18.52%
Therefore, the approximate percent increase in the price of the movie ticket is 18.52%.
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What is the surface area of the figure?
i believe the answer is B but im not sure
Answer:
582 ft²
Step-by-step explanation:
2(6x15)= 180
2(9x9)= 162
(9x4)= 36
(6x4)= 24
3(15x4)= 180
582 ft²
648 ft²
The number of eggs in the refrigerator e decreased by 2 equals 18. What’s the equation?
E-2=18 should be your answer
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❖ The correct answer is e - 2 = 18.
e is being decreased by 2 so we represent this as, -2. The problem says it equals 18 so therefore, the equation will be written as e - 2 = 18
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School A and B are competing in an academic contest. at the beginning of the final round, school A has 174 points and school B has 102 points, in the final round, correct answers earn 10 points and incorrect answers loose 6 points. school A hives the same number of correct and incorrect answers during the final round. school B gives no incorrect answers and the same number of correct answers as school A. the contest ends with te two schools tied. which equation models the scoring in the final round and outcome of the contest?
X = number of correct answers
Y = number of incorrect answers
School A has 174 points and school B has 102 points.
A = 174
B = 102
School A has the same number of correct and incorrect answers during the final round.
A = 174 + 10X - 6Y
School B gives no incorrect answers and the same number of correct answers as school A.
B = 102 + 10X
The contest ends with the two schools tied.
Score = 174 + 10X - 6Y = 102 + 10X
174 + 10X - 6Y = 102 + 10X
The diameter of a pizza is 12 inches. What is its area?
Answer: 113.0973 [tex]in^{2}[/tex]
Step-by-step explanation:
If the diameter of the circle is 12", then the radius is 6" (half the diameter), and the area "A" is (approximately) 3.14 * 6^2 or about 113.04 sq. in. The calculation is approximate because 3.14 is a rounded value for pi. But the correct answer is 113.0973 not 113.04 because it's giving you the answer compared to SQUARE, but we need the answer in Inches. So that was just an example.
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The area is approximately 113.097 square inches.
To find the area of a pizza with a diameter of 12 inches, we follow these steps:
First, find the radius of the pizza. The radius is half of the diameter. So, radius = diameter / 2 which gives: radius = 12 inches / 2 = 6 inches.Next, use the formula for the area of a circle: A = πr². Here, π (pi) is approximately 3.14159.Substitute the radius into the formula: A = π × (6 inches)² = π × 36 square inches.Finally, calculate the area: A = 3.14159 × 36 ≈ 113.097 square inches.Therefore, the area of the pizza is approximately 113.097 square inches.
State a true conclusion.
1) All rabbits like lettuce.
2) My pet is a rabbit. Conclusion:
I think it would be: "My pet rabbit likes lettuce."
I believe it would be 2) my pet is a rabbit.
Find all the zeros of the function f(x) = x^3 -2x^2 +16x -32
Answer:
Real zeros: x = 2All zeros: x = 2, x = -4i and x = 4iStep-by-step explanation:
[tex]f(x)=x^3-2x^2+16x-32\\\\\text{The zeros:}\\\\f(x)=0\Rightarrow x^3-2x^2+16x-32=0\\\\x^2(x-2)+16(x-2)=0\\\\(x-2)(x^2+16)=0\iff x-2=0\ \vee\ x^2+16=0\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}\\\\x^2+16=0\qquad\text{subtract 16 from both sides}\\x^2=-16<0\qquad\text{no real solutions}\\\\\text{In the set of the complex numbers}\\x^2=-16\to x=\pm\sqrt{-16}\\\boxed{x=-4i\ \vee\ x=4i}[/tex]
It took Joe 3 hours swimming at a speed of 12 miles per hour to swim along the Charles River. If Jennifer is swimming the same path along the Charles River at a speed of 9 miles per hour, how long will it take her to complete her swim?
Answer:
4 hours
Step-by-step explanation:
3 x 12 = 36
36/9 = 4
Answer:
4 hours
Step-by-step explanation:
3 x 12 = 36
36/9 = 4
A rectangular prism has a length of 11 centimeters, a width of 9 centimeters, and a height of 3 centimeters. Its volume is _______ cubic centimeters.
Answer:
297
Step-by-step explanation:
To find V or Volume to multiply all of the number so 11 time 9 times 3 equals 297. So V = 297
in 1-4 find unit price 8 pencils for 2.24
Answer:
The units price is [tex]\$0.28[/tex] per pencil
Step-by-step explanation:
we know that
To find the unit price divide the total cost by the total number of pencils
so
[tex]\frac{2.24}{8}\frac{\$}{pencils}=0.28\frac{\$}{pencil}[/tex]
A car is traveling at a rate of 99 kilometers per hour. What is the car's rate in meters per second? How many meters will the car travel in 10 seconds?
Answer:
The answer is 16.5 meters in 10 seconds
Step-by-step explanation:
First you divide 99 by 60 seconds
When you get 1.65 you multiply it by 10 second.
When you multiply 1.65 by 10 second you get 16.5 meters in 10 seconds
two numbers total 66 and have a difference of 22. Find the two numbers
➷ x + y = 66
y - x = 22 (rearrange for y)
y = x - 22 (substitute this into the top equation)
x + (x - 22) = 66
2x - 22 = 66
Add 22 to both sides
2x = 88
x = 44
The two numbers are 44 and 22
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The solution is x= 44 and y =22
Step-by-step explanation:See the image
Tristan rode his bike 3 2/3 miles on Saturday he rode 1 4/5 Mi on Sunday how many more miles did he ride on Saturday then on Sunday a.1 3/15 Miles b.1 3/5 c.1 13/15 d.2 13/15
Answer:
c. 1 13/15
Step-by-step explanation:
The best way to find out how much more Tristan rode his bike would be to subtract both of his distances together.
Saturday = [tex]3\dfrac{2}{3}[/tex]
Sunday = [tex]1\dfrac{4}{5}[/tex]
Now we actually have two different fractions with different denominators.
We can solve this first by converting the mixed numbers into improper fractions.
[tex]3\dfrac{2}{3}=\dfrac{9+2}{3}[/tex]
[tex]3\dfrac{2}{3}=\dfrac{11}{3}[/tex]
Now how did I do that?
First we take the denominator and multiply it to our whole number, then add the product to the numerator.
Let's proceed to the next mixed fraction.
[tex]1\dfrac{4}{5}=\dfrac{5+4}{5}[/tex]
[tex]1\dfrac{4}{5}=\dfrac{9}{5}[/tex]
We are then left with:
[tex]\dfrac{11}{3}-\dfrac{9}{5}[/tex]
Since we cannot subtract them directly because they have different denominators, we need to find the LCD of both denominators.
[tex](\dfrac{5}{5}) \dfrac{11}{3}-\dfrac{9}{5}(\dfrac{3}{3})[/tex]
[tex]\dfrac{55}{15}-\dfrac{27}{15}[/tex]
Now that they have similar denominators, we can then proceed to subtract them to each other.
[tex]\dfrac{55}{15}-\dfrac{27}{15}=\dfrac{28}{15}or1\dfrac{13}{15}[/tex]
add or subtract ( -2x^2-4x+13)+(12x^2+2x-25) show your work
First we need to simplify:
(-2x^2-4x+13 + (12x^2+2x-25) to get (−2x+12x )+(−4x+2x)+(13−25).
Simplify to get [tex]10x^2 - 2x - 12[/tex]
There is your answer^
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What is the quotient for the equation above?
Answer:
The correct answer option is C. 73.75.
Step-by-step explanation:
We are to perform division where 29.5 is the dividend while 0.4 is the divisor.
To make this division somehow easier, we can multiply both the dividend and the divisor by 10 to avoid the decimals.
So multiplying both the values with 10, we get:
[tex] \frac { 295 } { 4 } [/tex]
Now dividing 295 by 4, we get a quotient of 73.75.
To which real number subsets do the following real numbers belong?
0, 3, 7, 11, 15, 18
A.
irrational numbers and whole numbers
B.
integers and rational numbers
C.
natural numbers and irrational numbers
D.
integers and irrational numbers
pretty sure the answer is b
The real numbers 0, 3, 7, 11, 15, and 18 belong to the subsets of integers and rational numbers.
Explanation:The real number subsets to which each of the given numbers belong are as follows:
0 is a whole number, an integer, and a rational number.3 is a whole number, an integer, and a rational number.7 is a whole number, an integer, and a rational number.11 is a whole number, an integer, and a rational number.15 is a whole number, an integer, and a rational number.18 is a whole number, an integer, and a rational number.Therefore, the correct answer is B. integers and rational numbers.
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What percent of 85 is 72
Answer:
84.7058824 %
Step-by-step explanation:
Of means multiply and is means equals
P *85 = 72
Divide each side by 85
P *85/85 = 72/85
P = .847058824
Change from decimal form to percent form by multiplying by 100
P = .847058824 * 100
P = 84.7058824 %
Answer:
84.7058824 %
This is the correct answer.
How do you do this plz help me (10 points)
Answer:
Step-by-step explanation:
it easy tim will get 20 and sam will also get 20 so the ratio is 20;20 jope this helps you
William is drafting his fantasy basketball team. He needs to select one player for each position. The following table shows how many players are available for each position.
Position Number of players
Point guard 101010
Shooting guard 121212
Small forward 777
Power forward 222
Center 999
How many different teams could William draft?
Answer: 15120
Step-by-step explanation:
10×12×7×2×9=15120
Answer: 15120
Step-by-step explanation:
Given: The number of players at point guard = 10
The number of players at shooting guard = 12
The number of players at small forward = 7
The number of players at power forward = 2
The number of players at center = 9
Then, the number of different teams William could draft is given by :-
[tex]10*12*7*2*9=15120[/tex]
Hence, William could draft 15120 different teams.
On Monday Ned picked up 3/9 of a pound cans to recycle. On Tuesday he picked up 3/4 that amount. How many pounds did Ned pick up on Tuesday?
Answer:
1/4 lb
Step-by-step explanation:
9
Multiply: (3/9) times (3/4). This comes out to --------- = 1/4
9(4)
On Tuesday Ned picked up 1/4 lb of cans.
solve n^2+16n=17 by completing the square
Answer:
305 or N=1
Step-by-step explanation:
N=17, correct?
so what you do first is rewrite the equation:
17^2+16
which will equal:
305
if not and the equation is N^2+16=17
then you have to subtract the 16 first from 17
n^2=1
now you divide or whatever you call it XD
/n^2=/1
so the answer to N=1
What is 45,728 rounded to The nearest hundred
45,700
You either go up from 5-9 or down for 1-4.
Example:
56,891 to the nearest hundred.
An 8 is in the hundreds place so it will either be 56,800 or 56,900 depending on if you go up or down. Start at the ones place. The number is 1 so you take that down. Then you have 56,890. Next you go to the tens place. A 9 would go up so you then have 56,900. You are now in the hundreds place so you have solved the problem.
Answer:
45,700
Step-by-step explanation:
Go to the hundreds place and look at the number behind it. It's a 2. If you are rounding and the number behind it is 4 or less, you would keep it the same. If the number behind it is 5 or more, then you would round up. So, the answer is 45,700.